\section{Overview}
\label{sec:intro.overview}

In this thesis, we design efficient algorithms to enable positive
diffusion and good intervention strategies to control negative
diffusion. In Chapter \ref{chapter:discovery}, we study two nature
diffusion processes under organic dynamics, and show an almost tight
upper bound for both of these processes. In Chapter
\ref{chapter:token}, we study similar problems as in Chapter
\ref{chapter:discovery}, but under adversarial dynamics. We show an
lower bound for any token-forwarding algorithms under online
adversarial model, and design two efficient algorithms under offline
adversarial model. In Chapter \ref{chapter:game}, we study both
centralized and decentralized intervention strategies. We give an
$O(\log n)$ approximation algorithm for optimal centralized
intervention strategy. Then we show the existence of intervention
strategies in decentralized settings and compare their costs with the
optimal centralized strategy. In Chapter \ref{chapter:risk}, we extend
the study in Chapter \ref{chapter:game} to the presence of risk
behavior changes, and observe two interesting phenomena: 1) less
interventions can be more effective, and 2) targeted intervention
strategy can be worse than random intervention strategy. We conclude
in Chapter \ref{chapter:conclusion}.
